However, there are other, equivalent definitions of a circle.

We can freely use either equivalent definition above; indeed, in many cases, one of the two conditions is more useful than the other.

There are different equivalent definitions of a connection on .

An equivalent definition, one that I like better, is:"surface energy".

There are at least two equivalent definitions of a rigidity.

Other equivalent definitions can be given, for example, in terms of closed sets and closure.

In addition to the definition above, there is an equivalent definition.

Other, equivalent definitions are described in the article on gain graphs.

In this case, the following equivalent definition can be given:

There are two equivalent definitions of an ordered field.